Solve for $t$, $ -\dfrac{5t + 2}{2t + 5} = -\dfrac{8}{2t + 5} + \dfrac{1}{6t + 15} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2t + 5$ $2t + 5$ and $6t + 15$ The common denominator is $6t + 15$ To get $6t + 15$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ -\dfrac{5t + 2}{2t + 5} \times \dfrac{3}{3} = -\dfrac{15t + 6}{6t + 15} $ To get $6t + 15$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ -\dfrac{8}{2t + 5} \times \dfrac{3}{3} = -\dfrac{24}{6t + 15} $ The denominator of the third term is already $6t + 15$ , so we don't need to change it. This give us: $ -\dfrac{15t + 6}{6t + 15} = -\dfrac{24}{6t + 15} + \dfrac{1}{6t + 15} $ If we multiply both sides of the equation by $6t + 15$ , we get: $ -15t - 6 = -24 + 1$ $ -15t - 6 = -23$ $ -15t = -17 $ $ t = \dfrac{17}{15}$